Alkali halides are simple inorganic compounds extensively used as surface modifiers in optoelectronic devices. In perovskite solar cells (PSCs), they act as interlayers between the light absorber material and the charge selective layers improving their contact quality. They introduce surface dipoles that enable the fine tuning of the relative band alignment and passivate surface defects, a well-known drawback of hybrid organic-inorganic perovskites, that is responsible for most of the issues hampering the long-term performances. Reducing the thickness of such salt-based insulating layer might be beneficial in terms of charge transfer between the perovskite and the electron/hole transport layers. In this context, here we apply density functional theory (DFT) to characterize the structure and the electronic features of atom-thin layers of NaCl adsorbed on the methylammonium lead iodide (MAPI) perovskite. We analyze two different models of MAPI surface terminations and find unexpected structural reconstructions arising at the interface. Unexpectedly, we find an exotic honeycomb-like structuring of the salt, also recently observed in experiments on a diamond substrate. We also investigate how the salt affects the perovskite electronic properties that are key to control the charge dynamics at the interface. Moreover, we also assess the salt ability to improve the defect tolerance of the perovskite surface. With these results, we derive new hints regarding the potential benefits of using an atom-thin layer of alkali halides in PSCs.